////////////////////////////////////////////////////////////////////////
//
// Copyright (C) 2005-2021 The Octave Project Developers
//
// See the file COPYRIGHT.md in the top-level directory of this
// distribution or <https://octave.org/copyright/>.
//
// This file is part of Octave.
//
// Octave is free software: you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// Octave is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with Octave; see the file COPYING.  If not, see
// <https://www.gnu.org/licenses/>.
//
////////////////////////////////////////////////////////////////////////

#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif

#include "CMatrix.h"
#include "CSparse.h"
#include "MArray.h"
#include "dColVector.h"
#include "dMatrix.h"
#include "dSparse.h"
#include "lo-error.h"
#include "oct-locbuf.h"
#include "oct-sparse.h"
#include "quit.h"
#include "sparse-qr.h"

namespace octave
{
  namespace math
  {
#if defined (HAVE_CXSPARSE)
    template <typename SPARSE_T>
    class
    cxsparse_types
      { };

    template <>
    class
    cxsparse_types<SparseMatrix>
    {
    public:
      typedef CXSPARSE_DNAME (s) symbolic_type;
      typedef CXSPARSE_DNAME (n) numeric_type;
    };

    template <>
    class
    cxsparse_types<SparseComplexMatrix>
    {
    public:
      typedef CXSPARSE_ZNAME (s) symbolic_type;
      typedef CXSPARSE_ZNAME (n) numeric_type;
    };
#endif

    template <typename SPARSE_T>
    class sparse_qr<SPARSE_T>::sparse_qr_rep
    {
    public:

      sparse_qr_rep (const SPARSE_T& a, int order);

      // No copying!

      sparse_qr_rep (const sparse_qr_rep&) = delete;

      sparse_qr_rep& operator = (const sparse_qr_rep&) = delete;

      ~sparse_qr_rep (void);

      bool ok (void) const
      {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))
        return (m_H && m_Htau && m_HPinv && m_R && m_E);
#elif defined (HAVE_CXSPARSE)
        return (N && S);
#else
        return false;
#endif
      }

      SPARSE_T V (void) const;

      ColumnVector Pinv (void) const;

      ColumnVector P (void) const;

      ColumnVector E (void) const;

      SPARSE_T R (bool econ) const;

      typename SPARSE_T::dense_matrix_type
      C (const typename SPARSE_T::dense_matrix_type& b, bool econ = false);

      typename SPARSE_T::dense_matrix_type Q (bool econ = false);

      octave_idx_type nrows;
      octave_idx_type ncols;

#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      template <typename RHS_T, typename RET_T>
      RET_T solve (const RHS_T& b, octave_idx_type& info) const;

#endif

#if defined (HAVE_CXSPARSE)

      typename cxsparse_types<SPARSE_T>::symbolic_type *S;
      typename cxsparse_types<SPARSE_T>::numeric_type *N;

#endif

      template <typename RHS_T, typename RET_T>
      RET_T tall_solve (const RHS_T& b, octave_idx_type& info);

      template <typename RHS_T, typename RET_T>
      RET_T wide_solve (const RHS_T& b, octave_idx_type& info) const;

#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

    private:

      cholmod_common m_cc;
      cholmod_sparse *m_R;  // R factor
      // Column permutation for A. Fill-reducing ordering.
      SuiteSparse_long *m_E;
      cholmod_sparse *m_H;  // Householder vectors
      cholmod_dense *m_Htau;  // beta scalars
      SuiteSparse_long *m_HPinv;

#endif
    };

    template <typename SPARSE_T>
    ColumnVector
    sparse_qr<SPARSE_T>::sparse_qr_rep::Pinv (void) const
    {
#if defined (HAVE_CXSPARSE)

      ColumnVector ret (N->L->m);

      for (octave_idx_type i = 0; i < N->L->m; i++)
        ret.xelem (i) = S->pinv[i];

      return ret;

#else

      return ColumnVector ();

#endif
    }

    template <typename SPARSE_T>
    ColumnVector
    sparse_qr<SPARSE_T>::sparse_qr_rep::P (void) const
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      ColumnVector ret (nrows);

      // FIXME: Is ret.xelem (m_HPinv[i]) = i + 1 correct?
      for (octave_idx_type i = 0; i < nrows; i++)
        ret.xelem (from_suitesparse_long (m_HPinv[i])) = i + 1;

      return ret;

#elif defined (HAVE_CXSPARSE)

      ColumnVector ret (N->L->m);

      for (octave_idx_type i = 0; i < N->L->m; i++)
        ret.xelem (S->pinv[i]) = i;

      return ret;

#else

      return ColumnVector ();

#endif
    }

    template <typename SPARSE_T>
    ColumnVector
    sparse_qr<SPARSE_T>::sparse_qr_rep::E (void) const
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      ColumnVector ret (ncols);

      for (octave_idx_type i = 0; i < ncols; i++)
        ret(i) = from_suitesparse_long (m_E[i]) + 1;

      return ret;

#else

      return ColumnVector ();

#endif
    }

#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

    // Convert real sparse octave matrix to real sparse cholmod matrix.
    // Returns a "shallow" copy of a.
    static cholmod_sparse
    ros2rcs (const SparseMatrix& a)
    {
      cholmod_sparse A;

      octave_idx_type ncols = a.cols ();
      octave_idx_type nnz = a.nnz ();

      A.ncol = ncols;
      A.nrow = a.rows ();
      A.itype = CHOLMOD_LONG;
      A.nzmax = nnz;
      A.sorted = 0;
      A.packed = 1;
      A.stype = 0;
      A.xtype = CHOLMOD_REAL;
      A.dtype = CHOLMOD_DOUBLE;
      A.nz = nullptr;
      A.z = nullptr;
      if (sizeof (octave_idx_type) == sizeof (SuiteSparse_long))
        {
          A.p = reinterpret_cast<SuiteSparse_long *> (a.cidx ());
          A.i = reinterpret_cast<SuiteSparse_long *> (a.ridx ());
        }
      else
        {
          SuiteSparse_long *A_p;
          A_p = new SuiteSparse_long[ncols+1];
          for (octave_idx_type i = 0; i < ncols+1; i++)
            A_p[i] = a.cidx (i);
          A.p = A_p;
          SuiteSparse_long *A_i;
          A_i = new SuiteSparse_long[nnz];
          for (octave_idx_type i = 0; i < nnz; i++)
            A_i[i] = a.ridx (i);
          A.i = A_i;
        }
      A.x = const_cast<double *> (a.data ());

      return A;
    }

    // Convert complex sparse octave matrix to complex sparse cholmod matrix.
    // Returns a "shallow" copy of a.
    static cholmod_sparse
    cos2ccs (const SparseComplexMatrix& a)
    {
      cholmod_sparse A;

      octave_idx_type ncols = a.cols ();
      octave_idx_type nnz = a.nnz ();

      A.ncol = ncols;
      A.nrow = a.rows ();
      A.itype = CHOLMOD_LONG;
      A.nzmax = nnz;
      A.sorted = 0;
      A.packed = 1;
      A.stype = 0;
      A.xtype = CHOLMOD_COMPLEX;
      A.dtype = CHOLMOD_DOUBLE;
      A.nz = nullptr;
      A.z = nullptr;
      if (sizeof (octave_idx_type) == sizeof (SuiteSparse_long))
        {
          A.p = reinterpret_cast<SuiteSparse_long *> (a.cidx ());
          A.i = reinterpret_cast<SuiteSparse_long *> (a.ridx ());
        }
      else
        {
          SuiteSparse_long *A_p;
          A_p = new SuiteSparse_long[ncols+1];
          for (octave_idx_type i = 0; i < ncols+1; i++)
            A_p[i] = a.cidx (i);
          A.p = A_p;
          SuiteSparse_long *A_i;
          A_i = new SuiteSparse_long[nnz];
          for (octave_idx_type i = 0; i < nnz; i++)
            A_i[i] = a.ridx (i);
          A.i = A_i;
        }
      A.x = const_cast<Complex *>
                   (reinterpret_cast<const Complex *> (a.data ()));

      return A;
    }

    // Convert real dense octave matrix to complex dense cholmod matrix.
    // Returns a "deep" copy of a.
    static cholmod_dense*
    rod2ccd (const MArray<double>& a, cholmod_common *cc1)
    {
      cholmod_dense *A
        = cholmod_l_allocate_dense (a.rows (), a.cols (), a.rows(),
                                    CHOLMOD_COMPLEX, cc1);

      const double *a_x = a.data ();

      Complex *A_x = reinterpret_cast<Complex *> (A->x);
      for (octave_idx_type j = 0; j < a.cols() * a.rows() ; j++)
        A_x[j] = Complex (a_x[j], 0.0);

      return A;
    }

    // Convert real dense octave matrix to real dense cholmod matrix.
    // Returns a "shallow" copy of a.
    static cholmod_dense
    rod2rcd (const MArray<double> &a)
    {
      cholmod_dense A;

      A.ncol = a.cols ();
      A.nrow = a.rows ();
      A.nzmax = a.cols () * a.rows ();
      A.xtype = CHOLMOD_REAL;
      A.dtype = CHOLMOD_DOUBLE;
      A.z = nullptr;
      A.d = a.rows ();
      A.x = const_cast<double *> (a.data ());

      return A;
    }

    // Convert complex dense octave matrix to complex dense cholmod matrix.
    // Returns a "shallow" copy of a.
    static cholmod_dense
    cod2ccd (const ComplexMatrix &a)
    {
      cholmod_dense A;

      A.ncol = a.cols ();
      A.nrow = a.rows ();
      A.nzmax = a.cols () * a.rows ();
      A.xtype = CHOLMOD_COMPLEX;
      A.dtype = CHOLMOD_DOUBLE;
      A.z = nullptr;
      A.d = a.rows ();
      A.x = const_cast<Complex*> (reinterpret_cast<const Complex*> (a.data ()));

      return A;
    }

    // Convert real sparse cholmod matrix to real sparse octave matrix.
    // Returns a "shallow" copy of y.
    static SparseMatrix
    rcs2ros (const cholmod_sparse* y)
    {
      octave_idx_type nrow = from_size_t (y->nrow);
      octave_idx_type ncol = from_size_t (y->ncol);
      octave_idx_type nz = from_size_t (y->nzmax);
      SparseMatrix ret (nrow, ncol, nz);

      SuiteSparse_long *y_p = reinterpret_cast<SuiteSparse_long *> (y->p);
      for (octave_idx_type j = 0; j < ncol + 1; j++)
        ret.xcidx (j) = from_suitesparse_long (y_p[j]);

      SuiteSparse_long *y_i = reinterpret_cast<SuiteSparse_long *> (y->i);
      double *y_x = reinterpret_cast<double *> (y->x);
      for (octave_idx_type j = 0; j < nz; j++)
        {
          ret.xridx (j) = from_suitesparse_long (y_i[j]);
          ret.xdata (j) = y_x[j];
        }

      return ret;
    }

    // Convert complex sparse cholmod matrix to complex sparse octave matrix.
    // Returns a "deep" copy of a.
    static SparseComplexMatrix
    ccs2cos (const cholmod_sparse *a)
    {
      octave_idx_type nrow = from_size_t (a->nrow);
      octave_idx_type ncol = from_size_t (a->ncol);
      octave_idx_type nz = from_size_t (a->nzmax);
      SparseComplexMatrix ret (nrow, ncol, nz);

      SuiteSparse_long *a_p = reinterpret_cast<SuiteSparse_long *> (a->p);
      for (octave_idx_type j = 0; j < ncol + 1; j++)
        ret.xcidx(j) = from_suitesparse_long (a_p[j]);

      SuiteSparse_long *a_i = reinterpret_cast<SuiteSparse_long *> (a->i);
      Complex *a_x = reinterpret_cast<Complex *> (a->x);
      for (octave_idx_type j = 0; j < nz; j++)
        {
          ret.xridx(j) = from_suitesparse_long (a_i[j]);
          ret.xdata(j) = a_x[j];
        }

      return ret;
    }

    // Convert real sparse octave matrix to complex sparse cholmod matrix.
    // Returns a "deep" copy of a.
    static cholmod_sparse*
    ros2ccs (const SparseMatrix& a, cholmod_common *cc)
    {
      cholmod_sparse *A
        = cholmod_l_allocate_sparse (a.rows (), a.cols (), a.nnz (), 0, 1, 0,
                                     CHOLMOD_COMPLEX, cc);

      octave_idx_type ncol = a.cols ();
      SuiteSparse_long *A_p = reinterpret_cast<SuiteSparse_long *> (A->p);
      for (octave_idx_type j = 0; j < ncol + 1; j++)
        A_p[j] = a.cidx(j);

      const double *a_x = a.data ();
      Complex *A_x = reinterpret_cast<Complex *> (A->x);
      SuiteSparse_long *A_i = reinterpret_cast<SuiteSparse_long *> (A->i);
      for (octave_idx_type j = 0; j < a.nnz (); j++)
        {
          A_x[j] = Complex (a_x[j], 0.0);
          A_i[j] = a.ridx(j);
        }
      return A;
    }

    static suitesparse_integer
    suitesparse_long_to_suitesparse_integer (SuiteSparse_long x)
    {
      if (x < std::numeric_limits<suitesparse_integer>::min ()
          || x > std::numeric_limits<suitesparse_integer>::max ())
        (*current_liboctave_error_handler)
          ("integer dimension or index out of range for SuiteSparse's indexing type");

      return static_cast<suitesparse_integer> (x);
    }

    static void
    spqr_error_handler (const cholmod_common *cc)
    {
      if (cc->status >= 0)
        return;

      switch (cc->status)
        {
        case CHOLMOD_OUT_OF_MEMORY:
          (*current_liboctave_error_handler)
            ("sparse_qr: sparse matrix QR factorization failed"
             " - out of memory");
        case CHOLMOD_TOO_LARGE:
          (*current_liboctave_error_handler)
            ("sparse_qr: sparse matrix QR factorization failed"
             " - integer overflow occurred");
        default:
          (*current_liboctave_error_handler)
            ("sparse_qr: sparse matrix QR factorization failed"
             " - error %d", cc->status);
        }

      // FIXME: Free memory?
      // FIXME: Can cc-status > 0 (CHOLMOD_NOT_POSDEF, CHOLMOD_DSMALL) occur?
    }
#endif

    // Specializations.

    // Real-valued matrices.

    // Arguments for parameter order (taken from SuiteSparseQR documentation).
    // 0: fixed ordering 0 (no permutation of columns)
    // 1: natural ordering 1 (only singleton columns are permuted to the left of
    //    the matrix)
    // 2: colamd
    // 3:
    // 4: CHOLMOD best-effort (COLAMD, METIS,...)
    // 5: AMD(a'*a)
    // 6: metis(a'*a)
    // 7: SuiteSparseQR default ordering
    // 8: try COLAMD, AMD, and METIS; pick best
    // 9: try COLAMD and AMD; pick best
    //FIXME: What is order = 3?
    template <>
    sparse_qr<SparseMatrix>::sparse_qr_rep::sparse_qr_rep
    (const SparseMatrix& a, int order)
      : nrows (a.rows ()), ncols (a.columns ())
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))
      , m_cc (), m_R (nullptr), m_E (nullptr), m_H (nullptr), m_Htau (nullptr),
        m_HPinv (nullptr)
    {
      octave_idx_type nr = a.rows ();
      octave_idx_type nc = a.cols ();

      if (nr <= 0 || nc <= 0)
        (*current_liboctave_error_handler)
          ("matrix dimension with negative or zero size");

      if (order < 0 || order > 9)
        (*current_liboctave_error_handler)
          ("ordering %d is not supported by SPQR", order);

      cholmod_l_start (&m_cc);
      cholmod_sparse A = ros2rcs (a);

      SuiteSparseQR<double> (order, static_cast<double> (SPQR_DEFAULT_TOL),
                             static_cast<SuiteSparse_long> (A.nrow),
                             &A, &m_R, &m_E, &m_H, &m_HPinv, &m_Htau, &m_cc);
      spqr_error_handler (&m_cc);

      if (sizeof (octave_idx_type) != sizeof (SuiteSparse_long))
        {
          delete [] reinterpret_cast<SuiteSparse_long *> (A.p);
          delete [] reinterpret_cast<SuiteSparse_long *> (A.i);
        }
    }

#elif defined (HAVE_CXSPARSE)
      , S (nullptr), N (nullptr)
    {
      CXSPARSE_DNAME () A;

      A.nzmax = a.nnz ();
      A.m = nrows;
      A.n = ncols;
      // Cast away const on A, with full knowledge that CSparse won't touch it
      // Prevents the methods below making a copy of the data.
      A.p = const_cast<suitesparse_integer *>
              (to_suitesparse_intptr (a.cidx ()));
      A.i = const_cast<suitesparse_integer *>
              (to_suitesparse_intptr (a.ridx ()));
      A.x = const_cast<double *> (a.data ());
      A.nz = -1;

      S = CXSPARSE_DNAME (_sqr) (order, &A, 1);
      N = CXSPARSE_DNAME (_qr) (&A, S);

      if (! N)
        (*current_liboctave_error_handler)
          ("sparse_qr: sparse matrix QR factorization filled");

    }

#else

    {
      octave_unused_parameter (order);

      (*current_liboctave_error_handler)
        ("sparse_qr: support for SPQR or CXSparse was unavailable or disabled when liboctave was built");
    }

#endif

    template <>
    sparse_qr<SparseMatrix>::sparse_qr_rep::~sparse_qr_rep (void)
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      cholmod_l_free_sparse (&m_R, &m_cc);
      cholmod_l_free_sparse (&m_H, &m_cc);
      cholmod_l_free_dense (&m_Htau, &m_cc);
      free (m_E);  // FIXME: use cholmod_l_free
      free (m_HPinv);
      cholmod_l_finish (&m_cc);

#elif defined (HAVE_CXSPARSE)

      CXSPARSE_DNAME (_sfree) (S);
      CXSPARSE_DNAME (_nfree) (N);

#endif
    }

    template <>
    SparseMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::V (void) const
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      return rcs2ros (m_H);

#elif defined (HAVE_CXSPARSE)

      // Drop zeros from V and sort
      // FIXME: Is the double transpose to sort necessary?

      CXSPARSE_DNAME (_dropzeros) (N->L);
      CXSPARSE_DNAME () *D = CXSPARSE_DNAME (_transpose) (N->L, 1);
      CXSPARSE_DNAME (_spfree) (N->L);
      N->L = CXSPARSE_DNAME (_transpose) (D, 1);
      CXSPARSE_DNAME (_spfree) (D);

      octave_idx_type nc = N->L->n;
      octave_idx_type nz = N->L->nzmax;
      SparseMatrix ret (N->L->m, nc, nz);

      for (octave_idx_type j = 0; j < nc+1; j++)
        ret.xcidx (j) = N->L->p[j];

      for (octave_idx_type j = 0; j < nz; j++)
        {
          ret.xridx (j) = N->L->i[j];
          ret.xdata (j) = N->L->x[j];
        }

      return ret;

#else

      return SparseMatrix ();

#endif
    }

    template <>
    SparseMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::R (bool econ) const
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      octave_idx_type nr = static_cast<octave_idx_type> (m_R->nrow);
      octave_idx_type nc = static_cast<octave_idx_type> (m_R->ncol);
      octave_idx_type nz = static_cast<octave_idx_type> (m_R->nzmax);

      // FIXME: Does this work if econ = true?
      SparseMatrix ret ((econ ? (nc > nr ? nr : nc) : nr), nc, nz);
      SuiteSparse_long *Rp = reinterpret_cast<SuiteSparse_long *> (m_R->p);
      SuiteSparse_long *Ri = reinterpret_cast<SuiteSparse_long *> (m_R->i);

      for (octave_idx_type j = 0; j < nc + 1; j++)
        ret.xcidx (j) = from_suitesparse_long (Rp[j]);

      for (octave_idx_type j = 0; j < nz; j++)
        {
          ret.xridx (j) = from_suitesparse_long (Ri[j]);
          ret.xdata (j) = (reinterpret_cast<double *> (m_R->x))[j];
        }

      return ret;

#elif defined (HAVE_CXSPARSE)

      // Drop zeros from R and sort
      // FIXME: Is the double transpose to sort necessary?

      CXSPARSE_DNAME (_dropzeros) (N->U);
      CXSPARSE_DNAME () *D = CXSPARSE_DNAME (_transpose) (N->U, 1);
      CXSPARSE_DNAME (_spfree) (N->U);
      N->U = CXSPARSE_DNAME (_transpose) (D, 1);
      CXSPARSE_DNAME (_spfree) (D);

      octave_idx_type nc = N->U->n;
      octave_idx_type nz = N->U->nzmax;

      SparseMatrix ret ((econ ? (nc > nrows ? nrows : nc) : nrows), nc, nz);

      for (octave_idx_type j = 0; j < nc+1; j++)
        ret.xcidx (j) = N->U->p[j];

      for (octave_idx_type j = 0; j < nz; j++)
        {
          ret.xridx (j) = N->U->i[j];
          ret.xdata (j) = N->U->x[j];
        }

      return ret;

#else

      octave_unused_parameter (econ);

      return SparseMatrix ();

#endif
    }

    template <>
    Matrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::C (const Matrix &b, bool econ)
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))
      octave_idx_type nr = (econ
                            ? (ncols > nrows ? nrows : ncols)
                            : nrows);
      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();
      Matrix ret (nr, b_nc);

      if (nrows != b_nr)
        (*current_liboctave_error_handler)
          ("sparse_qr: matrix dimension mismatch");
      else if (b_nc <= 0 || b_nr <= 0)
        (*current_liboctave_error_handler)
          ("sparse_qr: matrix dimension with negative or zero size");

      cholmod_dense *QTB;  // Q' * B
      cholmod_dense B = rod2rcd (b);

      QTB = SuiteSparseQR_qmult<double> (SPQR_QTX, m_H, m_Htau, m_HPinv, &B,
                                         &m_cc);
      spqr_error_handler (&m_cc);

      // copy QTB into ret
      double *QTB_x = reinterpret_cast<double *> (QTB->x);
      double *ret_vec = reinterpret_cast<double *> (ret.fortran_vec ());
      for (octave_idx_type j = 0; j < b_nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          ret_vec[j * nr + i] = QTB_x[j * b_nr + i];

      cholmod_l_free_dense (&QTB, &m_cc);

      return ret;

#elif defined (HAVE_CXSPARSE)

      if (econ)
        (*current_liboctave_error_handler)
          ("sparse-qr: economy mode with CXSparse not supported");

      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();

      octave_idx_type nc = N->L->n;
      octave_idx_type nr = nrows;

      const double *bvec = b.data ();

      Matrix ret (b_nr, b_nc);
      double *vec = ret.fortran_vec ();

      if (nr < 0 || nc < 0 || nr != b_nr)
        (*current_liboctave_error_handler) ("matrix dimension mismatch");

      if (nr == 0 || nc == 0 || b_nc == 0)
        ret = Matrix (nc, b_nc, 0.0);
      else
        {
          OCTAVE_LOCAL_BUFFER (double, buf, S->m2);

          for (volatile octave_idx_type j = 0, idx = 0;
               j < b_nc;
               j++, idx += b_nr)
            {
              octave_quit ();

              for (octave_idx_type i = nr; i < S->m2; i++)
                buf[i] = 0.;

              volatile octave_idx_type nm = (nr < nc ? nr : nc);

              CXSPARSE_DNAME (_ipvec) (S->pinv, bvec + idx, buf, b_nr);

              for (volatile octave_idx_type i = 0; i < nm; i++)
                {
                  octave_quit ();

                  CXSPARSE_DNAME (_happly) (N->L, i, N->B[i], buf);
                }

              for (octave_idx_type i = 0; i < b_nr; i++)
                vec[i+idx] = buf[i];
            }
        }

      return ret;

#else

      octave_unused_parameter (b);
      octave_unused_parameter (econ);

      return Matrix ();

#endif
    }

    template <>
    Matrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::Q (bool econ)
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      octave_idx_type nc = (econ
                            ? (ncols > nrows ? nrows : ncols)
                            : nrows);
      Matrix ret (nrows, nc);
      cholmod_dense *q;

      // I is nrows x nrows identity matrix
      cholmod_dense *I
        = cholmod_l_allocate_dense (nrows, nrows, nrows, CHOLMOD_REAL, &m_cc);

      for (octave_idx_type i = 0; i < nrows * nrows; i++)
        (reinterpret_cast<double *> (I->x))[i] = 0.0;

      for (octave_idx_type i = 0; i < nrows; i++)
       (reinterpret_cast<double *> (I->x))[i * nrows + i] = 1.0;

      q = SuiteSparseQR_qmult<double> (SPQR_QX, m_H, m_Htau, m_HPinv, I, &m_cc);
      spqr_error_handler (&m_cc);

      double *q_x = reinterpret_cast<double *> (q->x);
      double *ret_vec = const_cast<double *> (ret.fortran_vec ());
      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nrows; i++)
          ret_vec[j * nrows + i] = q_x[j * nrows + i];

      cholmod_l_free_dense (&q, &m_cc);
      cholmod_l_free_dense (&I, &m_cc);

      return ret;

#elif defined (HAVE_CXSPARSE)

      if (econ)
        (*current_liboctave_error_handler)
          ("sparse-qr: economy mode with CXSparse not supported");

      octave_idx_type nc = N->L->n;
      octave_idx_type nr = nrows;
      Matrix ret (nr, nr);
      double *ret_vec = ret.fortran_vec ();

      if (nr < 0 || nc < 0)
        (*current_liboctave_error_handler) ("matrix dimension mismatch");

      if (nr == 0 || nc == 0)
        ret = Matrix (nc, nr, 0.0);
      else
        {
          OCTAVE_LOCAL_BUFFER (double, bvec, nr + 1);

          for (octave_idx_type i = 0; i < nr; i++)
            bvec[i] = 0.;

          OCTAVE_LOCAL_BUFFER (double, buf, S->m2);

          for (volatile octave_idx_type j = 0, idx = 0; j < nr; j++, idx += nr)
            {
              octave_quit ();

              bvec[j] = 1.0;
              for (octave_idx_type i = nr; i < S->m2; i++)
                buf[i] = 0.;

              volatile octave_idx_type nm = (nr < nc ? nr : nc);

              CXSPARSE_DNAME (_ipvec) (S->pinv, bvec, buf, nr);

              for (volatile octave_idx_type i = 0; i < nm; i++)
                {
                  octave_quit ();

                  CXSPARSE_DNAME (_happly) (N->L, i, N->B[i], buf);
                }

              for (octave_idx_type i = 0; i < nr; i++)
                ret_vec[i+idx] = buf[i];

              bvec[j] = 0.0;
            }
        }

      return ret.transpose ();

#else

      octave_unused_parameter (econ);

      return Matrix ();

#endif
    }

    template <>
    template <>
    Matrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::tall_solve<MArray<double>, Matrix>
    (const MArray<double>& b, octave_idx_type& info)
    {
      info = -1;

#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD) && defined (HAVE_CXSPARSE))

      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();
      Matrix x (ncols, b_nc);  // X = m_E'*(m_R\(Q'*B))

      if (nrows <= 0 || ncols <= 0 || b_nc <= 0 || b_nr <= 0)
        (*current_liboctave_error_handler)
          ("matrix dimension with negative or zero size");

      if (nrows < 0 || ncols < 0 || nrows != b_nr)
        (*current_liboctave_error_handler) ("matrix dimension mismatch");

      cholmod_dense *QTB;  // Q' * B
      cholmod_dense B = rod2rcd (b);

      // FIXME: Process b column by column as in the CXSPARSE version below.
      // This avoids a large dense matrix Q' * B in memory.
      QTB = SuiteSparseQR_qmult<double> (SPQR_QTX, m_H, m_Htau, m_HPinv, &B,
                                         &m_cc);

      spqr_error_handler (&m_cc);

      // convert m_R into CXSPARSE matrix R2
      CXSPARSE_DNAME (_sparse) R2;
      R2.n = ncols;
      R2.m = ncols;
      R2.nzmax = m_R->nzmax;
      R2.x = reinterpret_cast<double *> (m_R->x);
      suitesparse_integer *R2_p;
      suitesparse_integer *R2_i;
      if (sizeof (suitesparse_integer) == sizeof (SuiteSparse_long))
        {
          R2.p = reinterpret_cast<suitesparse_integer *> (m_R->p);
          R2.i = reinterpret_cast<suitesparse_integer *> (m_R->i);
        }
      else
        {
          R2_p = new suitesparse_integer[ncols+1];
          SuiteSparse_long * R_p = reinterpret_cast<SuiteSparse_long *> (m_R->p);
          for (octave_idx_type i = 0; i < ncols+1; i++)
            R2_p[i] = suitesparse_long_to_suitesparse_integer (R_p[i]);
          R2.p = R2_p;
          octave_idx_type nnz = m_R->nzmax;
          R2_i = new suitesparse_integer[nnz];
          SuiteSparse_long * R_i = reinterpret_cast<SuiteSparse_long *> (m_R->i);
          for (octave_idx_type i = 0; i < nnz; i++)
            R2_i[i] =  suitesparse_long_to_suitesparse_integer (R_i[i]);
          R2.i = R2_i;
        }
      R2.nz = -1;
      double *x_vec = const_cast<double *> (x.fortran_vec ());
      suitesparse_integer *E;
      if (sizeof (suitesparse_integer) != sizeof (SuiteSparse_long))
        {
          E = new suitesparse_integer [ncols];
          for (octave_idx_type i = 0; i < ncols; i++)
            E[i] = suitesparse_long_to_suitesparse_integer (m_E[i]);
        }
      else
        E = reinterpret_cast<suitesparse_integer *> (m_E);
      for (volatile octave_idx_type j = 0; j < b_nc; j++)
        {
          // fill x(:,j)
          // solve (m_R\(Q'*B(:,j)) and store result in QTB(:,j)
          CXSPARSE_DNAME (_usolve)
            (&R2, &(reinterpret_cast<double *> (QTB->x)[j * b_nr]));
          // x(:,j) = m_E' * (m_R\(Q'*B(:,j))
          CXSPARSE_DNAME (_ipvec)
            (E, &(reinterpret_cast<double *> (QTB->x)[j * b_nr]),
             &x_vec[j * ncols], ncols);
        }

      if (sizeof (suitesparse_integer) != sizeof (SuiteSparse_long))
        {
          delete [] R2_p;
          delete [] R2_i;
          delete [] E;
        }
      cholmod_l_free_dense (&QTB, &m_cc);

      info = 0;

      return x;

#elif defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      const double *bvec = b.data ();

      Matrix x (nc, b_nc);
      double *vec = x.fortran_vec ();

      OCTAVE_LOCAL_BUFFER (double, buf, S->m2);

      for (volatile octave_idx_type i = 0, idx = 0, bidx = 0; i < b_nc;
           i++, idx+=nc, bidx+=b_nr)
        {
          octave_quit ();

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_ipvec) (S->pinv, bvec + bidx, buf, nr);

          for (volatile octave_idx_type j = 0; j < nc; j++)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, vec + idx, nc);
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return Matrix ();

#endif
    }

    template <>
    template <>
    Matrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::wide_solve<MArray<double>, Matrix>
    (const MArray<double>& b, octave_idx_type& info) const
    {
      info = -1;
#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      const double *bvec = b.data ();

      Matrix x (nc, b_nc);
      double *vec = x.fortran_vec ();

      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (double, buf, nbuf);

      for (volatile octave_idx_type i = 0, idx = 0, bidx = 0; i < b_nc;
           i++, idx+=nc, bidx+=b_nr)
        {
          octave_quit ();

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_pvec) (S->q, bvec + bidx, buf, nr);
          CXSPARSE_DNAME (_utsolve) (N->U, buf);

          for (volatile octave_idx_type j = nr-1; j >= 0; j--)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_pvec) (S->pinv, buf, vec + idx, nc);
        }

      info = 0;

      return x;

#else
      octave_unused_parameter (b);

      return Matrix ();

#endif
    }

    template <>
    template <>
    SparseMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::tall_solve<SparseMatrix, SparseMatrix>
    (const SparseMatrix& b, octave_idx_type& info)
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();

      SparseMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, S->m2);

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            Xx[j] = b.xelem (j,i);

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_ipvec) (S->pinv, Xx, buf, nr);

          for (volatile octave_idx_type j = 0; j < nc; j++)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, Xx, nc);

          for (octave_idx_type j = 0; j < nc; j++)
            {
              double tmp = Xx[j];

              if (tmp != 0.0)
                {
                  if (ii == x_nz)
                    {
                      // Resize the sparse matrix
                      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
                      sz = (sz > 10 ? sz : 10) + x_nz;
                      x.change_capacity (sz);
                      x_nz = sz;
                    }

                  x.xdata (ii) = tmp;
                  x.xridx (ii++) = j;
                }
            }

          x.xcidx (i+1) = ii;
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return SparseMatrix ();

#endif
    }

    template <>
    template <>
    SparseMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::wide_solve<SparseMatrix, SparseMatrix>
    (const SparseMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();

      SparseMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;
      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, nbuf);

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            Xx[j] = b.xelem (j,i);

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_pvec) (S->q, Xx, buf, nr);
          CXSPARSE_DNAME (_utsolve) (N->U, buf);

          for (volatile octave_idx_type j = nr-1; j >= 0; j--)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_pvec) (S->pinv, buf, Xx, nc);

          for (octave_idx_type j = 0; j < nc; j++)
            {
              double tmp = Xx[j];

              if (tmp != 0.0)
                {
                  if (ii == x_nz)
                    {
                      // Resize the sparse matrix
                      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
                      sz = (sz > 10 ? sz : 10) + x_nz;
                      x.change_capacity (sz);
                      x_nz = sz;
                    }

                  x.xdata (ii) = tmp;
                  x.xridx (ii++) = j;
                }
            }

          x.xcidx (i+1) = ii;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::tall_solve<MArray<Complex>, ComplexMatrix>
    (const MArray<Complex>& b, octave_idx_type& info)
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      ComplexMatrix x (nc, b_nc);
      Complex *vec = x.fortran_vec ();

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, Xz, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, S->m2);

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            {
              Complex c = b.xelem (j,i);
              Xx[j] = c.real ();
              Xz[j] = c.imag ();
            }

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_ipvec) (S->pinv, Xx, buf, nr);

          for (volatile octave_idx_type j = 0; j < nc; j++)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, Xx, nc);

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_ipvec) (S->pinv, Xz, buf, nr);

          for (volatile octave_idx_type j = 0; j < nc; j++)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, Xz, nc);

          for (octave_idx_type j = 0; j < nc; j++)
            vec[j+idx] = Complex (Xx[j], Xz[j]);
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::wide_solve<MArray<Complex>, ComplexMatrix>
    (const MArray<Complex>& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      ComplexMatrix x (nc, b_nc);
      Complex *vec = x.fortran_vec ();

      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, Xz, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, nbuf);

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            {
              Complex c = b.xelem (j,i);
              Xx[j] = c.real ();
              Xz[j] = c.imag ();
            }

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_pvec) (S->q, Xx, buf, nr);
          CXSPARSE_DNAME (_utsolve) (N->U, buf);

          for (volatile octave_idx_type j = nr-1; j >= 0; j--)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_pvec) (S->pinv, buf, Xx, nc);

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_pvec) (S->q, Xz, buf, nr);
          CXSPARSE_DNAME (_utsolve) (N->U, buf);

          for (volatile octave_idx_type j = nr-1; j >= 0; j--)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_pvec) (S->pinv, buf, Xz, nc);

          for (octave_idx_type j = 0; j < nc; j++)
            vec[j+idx] = Complex (Xx[j], Xz[j]);
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    // Complex-valued matrices.

    template <>
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::sparse_qr_rep
    (const SparseComplexMatrix& a, int order)
      : nrows (a.rows ()), ncols (a.columns ())
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))
        , m_cc (), m_R (nullptr), m_E (nullptr), m_H (nullptr),
          m_Htau (nullptr), m_HPinv (nullptr)
    {
      octave_idx_type nr = a.rows ();
      octave_idx_type nc = a.cols ();

      if (nr <= 0 || nc <= 0)
        (*current_liboctave_error_handler)
          ("matrix dimension with negative or zero size");

      if (order < 0 || order > 9)
        (*current_liboctave_error_handler)
          ("ordering %d is not supported by SPQR", order);

      cholmod_l_start (&m_cc);
      cholmod_sparse A = cos2ccs (a);

      SuiteSparseQR<Complex> (order, static_cast<double> (SPQR_DEFAULT_TOL),
                              static_cast<SuiteSparse_long> (A.nrow),
                              &A, &m_R, &m_E, &m_H,
                              &m_HPinv, &m_Htau, &m_cc);
      spqr_error_handler (&m_cc);

      if (sizeof (octave_idx_type) != sizeof (SuiteSparse_long))
        {
          delete [] reinterpret_cast<SuiteSparse_long *> (A.p);
          delete [] reinterpret_cast<SuiteSparse_long *> (A.i);
        }
    }

#elif defined (HAVE_CXSPARSE)
        , S (nullptr), N (nullptr)
    {
      CXSPARSE_ZNAME () A;

      A.nzmax = a.nnz ();
      A.m = nrows;
      A.n = ncols;
      // Cast away const on A, with full knowledge that CSparse won't touch it
      // Prevents the methods below making a copy of the data.
      A.p = const_cast<suitesparse_integer *>
              (to_suitesparse_intptr (a.cidx ()));
      A.i = const_cast<suitesparse_integer *>
              (to_suitesparse_intptr (a.ridx ()));
      A.x = const_cast<cs_complex_t *>
              (reinterpret_cast<const cs_complex_t *> (a.data ()));
      A.nz = -1;

      S = CXSPARSE_ZNAME (_sqr) (order, &A, 1);
      N = CXSPARSE_ZNAME (_qr) (&A, S);

      if (! N)
        (*current_liboctave_error_handler)
          ("sparse_qr: sparse matrix QR factorization filled");

    }

#else

    {
      octave_unused_parameter (order);

      (*current_liboctave_error_handler)
        ("sparse_qr: support for CXSparse was unavailable or disabled when liboctave was built");
    }

#endif

    template <>
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::~sparse_qr_rep (void)
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      cholmod_l_free_sparse (&m_R, &m_cc);
      cholmod_l_free_sparse (&m_H, &m_cc);
      cholmod_l_free_dense (&m_Htau, &m_cc);
      free (m_E);  // FIXME: use cholmod_l_free
      free (m_HPinv);
      cholmod_l_finish (&m_cc);

#elif defined (HAVE_CXSPARSE)

      CXSPARSE_ZNAME (_sfree) (S);
      CXSPARSE_ZNAME (_nfree) (N);

#endif
    }

    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::V (void) const
    {
#if defined (HAVE_CXSPARSE)
      // Drop zeros from V and sort
      // FIXME: Is the double transpose to sort necessary?

      CXSPARSE_ZNAME (_dropzeros) (N->L);
      CXSPARSE_ZNAME () *D = CXSPARSE_ZNAME (_transpose) (N->L, 1);
      CXSPARSE_ZNAME (_spfree) (N->L);
      N->L = CXSPARSE_ZNAME (_transpose) (D, 1);
      CXSPARSE_ZNAME (_spfree) (D);

      octave_idx_type nc = N->L->n;
      octave_idx_type nz = N->L->nzmax;
      SparseComplexMatrix ret (N->L->m, nc, nz);

      for (octave_idx_type j = 0; j < nc+1; j++)
        ret.xcidx (j) = N->L->p[j];

      for (octave_idx_type j = 0; j < nz; j++)
        {
          ret.xridx (j) = N->L->i[j];
          ret.xdata (j) = reinterpret_cast<Complex *> (N->L->x)[j];
        }

      return ret;

#else

      return SparseComplexMatrix ();

#endif
    }

    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::R (bool econ) const
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      octave_idx_type nr = from_size_t (m_R->nrow);
      octave_idx_type nc = from_size_t (m_R->ncol);
      octave_idx_type nz = from_size_t (m_R->nzmax);

      // FIXME: Does this work if econ = true?
      SparseComplexMatrix ret ((econ ? (nc > nr ? nr : nc) : nr), nc, nz);
      SuiteSparse_long *Rp = reinterpret_cast<SuiteSparse_long *> (m_R->p);
      SuiteSparse_long *Ri = reinterpret_cast<SuiteSparse_long *> (m_R->i);

      for (octave_idx_type j = 0; j < nc + 1; j++)
        ret.xcidx (j) = from_suitesparse_long (Rp[j]);

      for (octave_idx_type j = 0; j < nz; j++)
        {
          ret.xridx (j) = from_suitesparse_long (Ri[j]);
          ret.xdata (j) = (reinterpret_cast<Complex *> (m_R->x))[j];
        }

      return ret;

#elif defined (HAVE_CXSPARSE)

      // Drop zeros from R and sort
      // FIXME: Is the double transpose to sort necessary?

      CXSPARSE_ZNAME (_dropzeros) (N->U);
      CXSPARSE_ZNAME () *D = CXSPARSE_ZNAME (_transpose) (N->U, 1);
      CXSPARSE_ZNAME (_spfree) (N->U);
      N->U = CXSPARSE_ZNAME (_transpose) (D, 1);
      CXSPARSE_ZNAME (_spfree) (D);

      octave_idx_type nc = N->U->n;
      octave_idx_type nz = N->U->nzmax;

      SparseComplexMatrix ret ((econ ? (nc > nrows ? nrows : nc) : nrows),
                               nc, nz);

      for (octave_idx_type j = 0; j < nc+1; j++)
        ret.xcidx (j) = N->U->p[j];

      for (octave_idx_type j = 0; j < nz; j++)
        {
          ret.xridx (j) = N->U->i[j];
          ret.xdata (j) = reinterpret_cast<Complex *>(N->U->x)[j];
        }

      return ret;

#else

      octave_unused_parameter (econ);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::C
    (const ComplexMatrix& b, bool econ)
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      // FIXME: not tested
      octave_idx_type nr = (econ
                            ? (ncols > nrows ? nrows : ncols)
                            : nrows);
      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();
      ComplexMatrix ret (nr, b_nc);

      if (nrows != b_nr)
        (*current_liboctave_error_handler) ("matrix dimension mismatch");

      if (b_nc <= 0 || b_nr <= 0)
        (*current_liboctave_error_handler)
          ("matrix dimension with negative or zero size");

      cholmod_dense *QTB;  // Q' * B
      cholmod_dense B = cod2ccd (b);

      QTB = SuiteSparseQR_qmult<Complex> (SPQR_QTX, m_H, m_Htau, m_HPinv, &B,
                                          &m_cc);
      spqr_error_handler (&m_cc);

      // copy QTB into ret
      Complex *QTB_x = reinterpret_cast<Complex *> (QTB->x);
      Complex *ret_vec = reinterpret_cast<Complex *> (ret.fortran_vec ());
      for (octave_idx_type j = 0; j < b_nc; j++)
        for (octave_idx_type i = 0; i < nr; i++)
          ret_vec[j * nr + i] = QTB_x[j * b_nr + i];

      cholmod_l_free_dense (&QTB, &m_cc);

      return ret;

#elif defined (HAVE_CXSPARSE)

      if (econ)
        (*current_liboctave_error_handler)
          ("sparse-qr: economy mode with CXSparse not supported");

      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();
      octave_idx_type nc = N->L->n;
      octave_idx_type nr = nrows;
      const cs_complex_t *bvec
        = reinterpret_cast<const cs_complex_t *> (b.data ());
      ComplexMatrix ret (b_nr, b_nc);
      Complex *vec = ret.fortran_vec ();

      if (nr < 0 || nc < 0 || nr != b_nr)
        (*current_liboctave_error_handler) ("matrix dimension mismatch");

      if (nr == 0 || nc == 0 || b_nc == 0)
        ret = ComplexMatrix (nc, b_nc, Complex (0.0, 0.0));
      else
        {
          OCTAVE_LOCAL_BUFFER (Complex, buf, S->m2);

          for (volatile octave_idx_type j = 0, idx = 0;
               j < b_nc;
               j++, idx += b_nr)
            {
              octave_quit ();

              volatile octave_idx_type nm = (nr < nc ? nr : nc);

              CXSPARSE_ZNAME (_ipvec) (S->pinv, bvec + idx,
                                       reinterpret_cast<cs_complex_t *> (buf),
                                       b_nr);

              for (volatile octave_idx_type i = 0; i < nm; i++)
                {
                  octave_quit ();

                  CXSPARSE_ZNAME (_happly) (N->L, i, N->B[i],
                                            reinterpret_cast<cs_complex_t *> (buf));
                }

              for (octave_idx_type i = 0; i < b_nr; i++)
                vec[i+idx] = buf[i];
            }
        }

      return ret;

#else

      octave_unused_parameter (b);
      octave_unused_parameter (econ);

      return ComplexMatrix ();

#endif
    }

    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::Q (bool econ)
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      octave_idx_type nc = (econ
                            ? (ncols > nrows ? nrows : ncols)
                            : nrows);
      ComplexMatrix ret (nrows, nc);
      cholmod_dense *q;

      // I is nrows x nrows identity matrix
      cholmod_dense *I
        = reinterpret_cast<cholmod_dense *>
            (cholmod_l_allocate_dense (nrows, nrows, nrows, CHOLMOD_COMPLEX, &m_cc));

      for (octave_idx_type i = 0; i < nrows * nrows; i++)
        (reinterpret_cast<Complex *> (I->x))[i] = 0.0;

      for (octave_idx_type i = 0; i < nrows; i++)
        (reinterpret_cast<Complex *> (I->x))[i * nrows + i] = 1.0;

      q = SuiteSparseQR_qmult<Complex> (SPQR_QX, m_H, m_Htau, m_HPinv, I,
                                        &m_cc);
      spqr_error_handler (&m_cc);

      Complex *q_x = reinterpret_cast<Complex *> (q->x);
      Complex *ret_vec = const_cast<Complex*> (ret.fortran_vec ());

      for (octave_idx_type j = 0; j < nc; j++)
        for (octave_idx_type i = 0; i < nrows; i++)
          ret_vec[j * nrows + i] = q_x[j * nrows + i];

      cholmod_l_free_dense (&q, &m_cc);
      cholmod_l_free_dense (&I, &m_cc);

      return ret;

#elif defined (HAVE_CXSPARSE)

      if (econ)
        (*current_liboctave_error_handler)
          ("sparse-qr: economy mode with CXSparse not supported");

      octave_idx_type nc = N->L->n;
      octave_idx_type nr = nrows;
      ComplexMatrix ret (nr, nr);
      Complex *vec = ret.fortran_vec ();

      if (nr < 0 || nc < 0)
        (*current_liboctave_error_handler) ("matrix dimension mismatch");

      if (nr == 0 || nc == 0)
        ret = ComplexMatrix (nc, nr, Complex (0.0, 0.0));
      else
        {
          OCTAVE_LOCAL_BUFFER (cs_complex_t, bvec, nr);

          for (octave_idx_type i = 0; i < nr; i++)
            bvec[i] = cs_complex_t (0.0, 0.0);

          OCTAVE_LOCAL_BUFFER (Complex, buf, S->m2);

          for (volatile octave_idx_type j = 0, idx = 0; j < nr; j++, idx+=nr)
            {
              octave_quit ();

              bvec[j] = cs_complex_t (1.0, 0.0);

              volatile octave_idx_type nm = (nr < nc ? nr : nc);

              CXSPARSE_ZNAME (_ipvec) (S->pinv, bvec,
                                       reinterpret_cast<cs_complex_t *> (buf),
                                       nr);

              for (volatile octave_idx_type i = 0; i < nm; i++)
                {
                  octave_quit ();

                  CXSPARSE_ZNAME (_happly) (N->L, i, N->B[i],
                                            reinterpret_cast<cs_complex_t *> (buf));
                }

              for (octave_idx_type i = 0; i < nr; i++)
                vec[i+idx] = buf[i];

              bvec[j] = cs_complex_t (0.0, 0.0);
            }
        }

      return ret.hermitian ();

#else

      octave_unused_parameter (econ);

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::tall_solve<SparseComplexMatrix,
                                                       SparseComplexMatrix>
      (const SparseComplexMatrix& b, octave_idx_type& info)
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, Xz, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, S->m2);

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            {
              Complex c = b.xelem (j,i);
              Xx[j] = c.real ();
              Xz[j] = c.imag ();
            }

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_ipvec) (S->pinv, Xx, buf, nr);

          for (volatile octave_idx_type j = 0; j < nc; j++)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, Xx, nc);

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_ipvec) (S->pinv, Xz, buf, nr);

          for (volatile octave_idx_type j = 0; j < nc; j++)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, Xz, nc);

          for (octave_idx_type j = 0; j < nc; j++)
            {
              Complex tmp = Complex (Xx[j], Xz[j]);

              if (tmp != 0.0)
                {
                  if (ii == x_nz)
                    {
                      // Resize the sparse matrix
                      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
                      sz = (sz > 10 ? sz : 10) + x_nz;
                      x.change_capacity (sz);
                      x_nz = sz;
                    }

                  x.xdata (ii) = tmp;
                  x.xridx (ii++) = j;
                }
            }

          x.xcidx (i+1) = ii;
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::wide_solve<SparseComplexMatrix,
                                                       SparseComplexMatrix>
      (const SparseComplexMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;
      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, Xz, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, nbuf);

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            {
              Complex c = b.xelem (j,i);
              Xx[j] = c.real ();
              Xz[j] = c.imag ();
            }

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_pvec) (S->q, Xx, buf, nr);
          CXSPARSE_DNAME (_utsolve) (N->U, buf);

          for (volatile octave_idx_type j = nr-1; j >= 0; j--)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_pvec) (S->pinv, buf, Xx, nc);

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_pvec) (S->q, Xz, buf, nr);
          CXSPARSE_DNAME (_utsolve) (N->U, buf);

          for (volatile octave_idx_type j = nr-1; j >= 0; j--)
            {
              octave_quit ();

              CXSPARSE_DNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_DNAME (_pvec) (S->pinv, buf, Xz, nc);

          for (octave_idx_type j = 0; j < nc; j++)
            {
              Complex tmp = Complex (Xx[j], Xz[j]);

              if (tmp != 0.0)
                {
                  if (ii == x_nz)
                    {
                      // Resize the sparse matrix
                      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
                      sz = (sz > 10 ? sz : 10) + x_nz;
                      x.change_capacity (sz);
                      x_nz = sz;
                    }

                  x.xdata (ii) = tmp;
                  x.xridx (ii++) = j;
                }
            }

          x.xcidx (i+1) = ii;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::tall_solve<MArray<double>,
                                                              ComplexMatrix>
      (const MArray<double>& b, octave_idx_type& info)
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      ComplexMatrix x (nc, b_nc);
      cs_complex_t *vec = reinterpret_cast<cs_complex_t *> (x.fortran_vec ());

      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, S->m2);
      OCTAVE_LOCAL_BUFFER (Complex, Xx, b_nr);

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            Xx[j] = b.xelem (j,i);

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          CXSPARSE_ZNAME (_ipvec) (S->pinv,
                                   reinterpret_cast<cs_complex_t *>(Xx),
                                   buf, nr);

          for (volatile octave_idx_type j = 0; j < nc; j++)
            {
              octave_quit ();

              CXSPARSE_ZNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_ZNAME (_usolve) (N->U, buf);
          CXSPARSE_ZNAME (_ipvec) (S->q, buf, vec + idx, nc);
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::wide_solve<MArray<double>,
                                                              ComplexMatrix>
      (const MArray<double>& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseComplexMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      ComplexMatrix x (nc, b_nc);
      cs_complex_t *vec = reinterpret_cast<cs_complex_t *> (x.fortran_vec ());

      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, nbuf);
      OCTAVE_LOCAL_BUFFER (Complex, Xx, b_nr);
      OCTAVE_LOCAL_BUFFER (double, B, nr);

      for (octave_idx_type i = 0; i < nr; i++)
        B[i] = N->B[i];

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            Xx[j] = b.xelem (j,i);

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          CXSPARSE_ZNAME (_pvec) (S->q, reinterpret_cast<cs_complex_t *> (Xx),
                                  buf, nr);
          CXSPARSE_ZNAME (_utsolve) (N->U, buf);

          for (volatile octave_idx_type j = nr-1; j >= 0; j--)
            {
              octave_quit ();

              CXSPARSE_ZNAME (_happly) (N->L, j, B[j], buf);
            }

          CXSPARSE_ZNAME (_pvec) (S->pinv, buf, vec + idx, nc);
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::tall_solve<SparseMatrix,
                                                              SparseComplexMatrix>
      (const SparseMatrix& b, octave_idx_type& info)
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;

      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, S->m2);

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            Xx[j] = b.xelem (j,i);

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          CXSPARSE_ZNAME (_ipvec) (S->pinv,
                                   reinterpret_cast<cs_complex_t *> (Xx),
                                   buf, nr);

          for (volatile octave_idx_type j = 0; j < nc; j++)
            {
              octave_quit ();

              CXSPARSE_ZNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_ZNAME (_usolve) (N->U, buf);
          CXSPARSE_ZNAME (_ipvec) (S->q, buf,
                                   reinterpret_cast<cs_complex_t *> (Xx),
                                   nc);

          for (octave_idx_type j = 0; j < nc; j++)
            {
              Complex tmp = Xx[j];

              if (tmp != 0.0)
                {
                  if (ii == x_nz)
                    {
                      // Resize the sparse matrix
                      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
                      sz = (sz > 10 ? sz : 10) + x_nz;
                      x.change_capacity (sz);
                      x_nz = sz;
                    }

                  x.xdata (ii) = tmp;
                  x.xridx (ii++) = j;
                }
            }

          x.xcidx (i+1) = ii;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::wide_solve<SparseMatrix,
                                                              SparseComplexMatrix>
      (const SparseMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseComplexMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;
      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, nbuf);
      OCTAVE_LOCAL_BUFFER (double, B, nr);

      for (octave_idx_type i = 0; i < nr; i++)
        B[i] = N->B[i];

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            Xx[j] = b.xelem (j,i);

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          CXSPARSE_ZNAME (_pvec) (S->q,
                                  reinterpret_cast<cs_complex_t *> (Xx),
                                  buf, nr);
          CXSPARSE_ZNAME (_utsolve) (N->U, buf);

          for (volatile octave_idx_type j = nr-1; j >= 0; j--)
            {
              octave_quit ();

              CXSPARSE_ZNAME (_happly) (N->L, j, B[j], buf);
            }

          CXSPARSE_ZNAME (_pvec) (S->pinv, buf,
                                  reinterpret_cast<cs_complex_t *> (Xx),
                                  nc);

          for (octave_idx_type j = 0; j < nc; j++)
            {
              Complex tmp = Xx[j];

              if (tmp != 0.0)
                {
                  if (ii == x_nz)
                    {
                      // Resize the sparse matrix
                      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
                      sz = (sz > 10 ? sz : 10) + x_nz;
                      x.change_capacity (sz);
                      x_nz = sz;
                    }

                  x.xdata (ii) = tmp;
                  x.xridx (ii++) = j;
                }
            }

          x.xcidx (i+1) = ii;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::tall_solve<MArray<Complex>,
                                                              ComplexMatrix>
      (const MArray<Complex>& b, octave_idx_type& info)
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      const cs_complex_t *bvec = reinterpret_cast<const cs_complex_t *>
                                 (b.data ());

      ComplexMatrix x (nc, b_nc);
      cs_complex_t *vec = reinterpret_cast<cs_complex_t *>
                          (x.fortran_vec ());

      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, S->m2);

      for (volatile octave_idx_type i = 0, idx = 0, bidx = 0; i < b_nc;
           i++, idx+=nc, bidx+=b_nr)
        {
          octave_quit ();

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          CXSPARSE_ZNAME (_ipvec) (S->pinv, bvec + bidx, buf, nr);

          for (volatile octave_idx_type j = 0; j < nc; j++)
            {
              octave_quit ();

              CXSPARSE_ZNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_ZNAME (_usolve) (N->U, buf);
          CXSPARSE_ZNAME (_ipvec) (S->q, buf, vec + idx, nc);
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::wide_solve<MArray<Complex>,
                                                              ComplexMatrix>
      (const MArray<Complex>& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseComplexMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      const cs_complex_t *bvec = reinterpret_cast<const cs_complex_t *>
                                 (b.data ());

      ComplexMatrix x (nc, b_nc);
      cs_complex_t *vec = reinterpret_cast<cs_complex_t *> (x.fortran_vec ());

      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, nbuf);
      OCTAVE_LOCAL_BUFFER (double, B, nr);

      for (octave_idx_type i = 0; i < nr; i++)
        B[i] = N->B[i];

      for (volatile octave_idx_type i = 0, idx = 0, bidx = 0; i < b_nc;
           i++, idx+=nc, bidx+=b_nr)
        {
          octave_quit ();

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          CXSPARSE_ZNAME (_pvec) (S->q, bvec + bidx, buf, nr);
          CXSPARSE_ZNAME (_utsolve) (N->U, buf);

          for (volatile octave_idx_type j = nr-1; j >= 0; j--)
            {
              octave_quit ();

              CXSPARSE_ZNAME (_happly) (N->L, j, B[j], buf);
            }

          CXSPARSE_ZNAME (_pvec) (S->pinv, buf, vec + idx, nc);
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::tall_solve<SparseComplexMatrix,
                                                              SparseComplexMatrix>
      (const SparseComplexMatrix& b, octave_idx_type& info)
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;

      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, S->m2);

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            Xx[j] = b.xelem (j,i);

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          CXSPARSE_ZNAME (_ipvec) (S->pinv,
                                   reinterpret_cast<cs_complex_t *> (Xx),
                                   buf, nr);

          for (volatile octave_idx_type j = 0; j < nc; j++)
            {
              octave_quit ();

              CXSPARSE_ZNAME (_happly) (N->L, j, N->B[j], buf);
            }

          CXSPARSE_ZNAME (_usolve) (N->U, buf);
          CXSPARSE_ZNAME (_ipvec) (S->q, buf,
                                   reinterpret_cast<cs_complex_t *> (Xx),
                                   nc);

          for (octave_idx_type j = 0; j < nc; j++)
            {
              Complex tmp = Xx[j];

              if (tmp != 0.0)
                {
                  if (ii == x_nz)
                    {
                      // Resize the sparse matrix
                      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
                      sz = (sz > 10 ? sz : 10) + x_nz;
                      x.change_capacity (sz);
                      x_nz = sz;
                    }

                  x.xdata (ii) = tmp;
                  x.xridx (ii++) = j;
                }
            }

          x.xcidx (i+1) = ii;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::wide_solve<SparseComplexMatrix,
                                                              SparseComplexMatrix>
      (const SparseComplexMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseComplexMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;
      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, nbuf);
      OCTAVE_LOCAL_BUFFER (double, B, nr);

      for (octave_idx_type i = 0; i < nr; i++)
        B[i] = N->B[i];

      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
        {
          octave_quit ();

          for (octave_idx_type j = 0; j < b_nr; j++)
            Xx[j] = b.xelem (j,i);

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          CXSPARSE_ZNAME (_pvec) (S->q, reinterpret_cast<cs_complex_t *>(Xx),
                                  buf, nr);
          CXSPARSE_ZNAME (_utsolve) (N->U, buf);

          for (volatile octave_idx_type j = nr-1; j >= 0; j--)
            {
              octave_quit ();

              CXSPARSE_ZNAME (_happly) (N->L, j, B[j], buf);
            }

          CXSPARSE_ZNAME (_pvec) (S->pinv, buf,
                                  reinterpret_cast<cs_complex_t *>(Xx), nc);

          for (octave_idx_type j = 0; j < nc; j++)
            {
              Complex tmp = Xx[j];

              if (tmp != 0.0)
                {
                  if (ii == x_nz)
                    {
                      // Resize the sparse matrix
                      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
                      sz = (sz > 10 ? sz : 10) + x_nz;
                      x.change_capacity (sz);
                      x_nz = sz;
                    }

                  x.xdata (ii) = tmp;
                  x.xridx (ii++) = j;
                }
            }

          x.xcidx (i+1) = ii;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <typename SPARSE_T>
    sparse_qr<SPARSE_T>::sparse_qr (void)
      : m_rep (new sparse_qr_rep (SPARSE_T (), 0))
    { }

    template <typename SPARSE_T>
    sparse_qr<SPARSE_T>::sparse_qr (const SPARSE_T& a, int order)
      : m_rep (new sparse_qr_rep (a, order))
    { }

    template <typename SPARSE_T>
    bool
    sparse_qr<SPARSE_T>::ok (void) const
    {
      return m_rep->ok ();
    }

    template <typename SPARSE_T>
    SPARSE_T
    sparse_qr<SPARSE_T>::V (void) const
    {
      return m_rep->V ();
    }

    template <typename SPARSE_T>
    ColumnVector
    sparse_qr<SPARSE_T>::Pinv (void) const
    {
      return m_rep->P ();
    }

    template <typename SPARSE_T>
    ColumnVector
    sparse_qr<SPARSE_T>::P (void) const
    {
      return m_rep->P ();
    }

    template <typename SPARSE_T>
    ColumnVector
    sparse_qr<SPARSE_T>::E (void) const
    {
      return m_rep->E();
    }


    template <typename SPARSE_T>
    SparseMatrix
    sparse_qr<SPARSE_T>::E_MAT (void) const
    {
      ColumnVector perm = m_rep->E ();
      octave_idx_type nrows = perm.rows ();
      SparseMatrix ret (nrows,nrows,nrows);
      for (octave_idx_type i = 0; i < nrows; i++)
        ret(perm(i) - 1,i) = 1.0;
      return ret;
    }


    template <typename SPARSE_T>
    SPARSE_T
    sparse_qr<SPARSE_T>::R (bool econ) const
    {
      return m_rep->R (econ);
    }

    template <typename SPARSE_T>
    typename SPARSE_T::dense_matrix_type
    sparse_qr<SPARSE_T>::C (const typename SPARSE_T::dense_matrix_type& b,
                            bool econ) const
    {
      return m_rep->C (b, econ);
    }

    template <typename SPARSE_T>
    typename SPARSE_T::dense_matrix_type
    sparse_qr<SPARSE_T>::Q (bool econ) const
    {
      return m_rep->Q (econ);
    }

#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))
    //specializations of function min2norm_solve
    template <>
    template <>
    OCTAVE_API Matrix
    sparse_qr<SparseMatrix>::min2norm_solve<MArray<double>, Matrix>
    (const SparseMatrix& a, const MArray<double>& b,
     octave_idx_type& info, int order)
    {
      info = -1;
      octave_idx_type b_nc = b.cols ();
      octave_idx_type nc = a.cols ();
      Matrix x (nc, b_nc);
      cholmod_common cc;

      cholmod_l_start (&cc);
      cholmod_sparse A = ros2rcs (a);
      cholmod_dense B = rod2rcd (b);
      cholmod_dense *X;

      X = SuiteSparseQR_min2norm<double> (order, SPQR_DEFAULT_TOL, &A, &B, &cc);
      spqr_error_handler (&cc);

      double *vec = x.fortran_vec ();
      for (volatile octave_idx_type i = 0; i < nc * b_nc; i++)
        vec[i] = reinterpret_cast<double *> (X->x)[i];

      info = 0;
      if (sizeof (octave_idx_type) != sizeof (SuiteSparse_long))
        {
          delete [] reinterpret_cast<SuiteSparse_long *> (A.p);
          delete [] reinterpret_cast<SuiteSparse_long *> (A.i);
        }
      cholmod_l_finish (&cc);

      return x;

    }

    template <>
    template <>
    OCTAVE_API SparseMatrix
    sparse_qr<SparseMatrix>::min2norm_solve<SparseMatrix, SparseMatrix>
    (const SparseMatrix& a, const SparseMatrix& b, octave_idx_type& info,
     int order)
    {
      info = -1;
      SparseMatrix x;
      cholmod_common cc;

      cholmod_l_start (&cc);
      cholmod_sparse A = ros2rcs (a);
      cholmod_sparse B = ros2rcs (b);
      cholmod_sparse *X;

      X = SuiteSparseQR_min2norm<double> (order, SPQR_DEFAULT_TOL, &A, &B, &cc);
      spqr_error_handler (&cc);

      if (sizeof (octave_idx_type) != sizeof (SuiteSparse_long))
        {
          delete [] reinterpret_cast<SuiteSparse_long *> (A.p);
          delete [] reinterpret_cast<SuiteSparse_long *> (A.i);
          delete [] reinterpret_cast<SuiteSparse_long *> (B.p);
          delete [] reinterpret_cast<SuiteSparse_long *> (B.i);
        }

      x = rcs2ros (X);
      cholmod_l_finish (&cc);
      info = 0;

      return x;

    }

    template <>
    template <>
    OCTAVE_API ComplexMatrix
    sparse_qr<SparseMatrix>::min2norm_solve<MArray<Complex>, ComplexMatrix>
    (const SparseMatrix& a, const MArray<Complex>& b,
     octave_idx_type& info, int order)
    {
      info = -1;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type nc = a.cols ();

      ComplexMatrix x (nc, b_nc);

      cholmod_common cc;

      cholmod_l_start (&cc);

      cholmod_sparse *A = ros2ccs (a, &cc);
      cholmod_dense B = cod2ccd (b);
      cholmod_dense *X;

      X = SuiteSparseQR_min2norm<Complex> (order, SPQR_DEFAULT_TOL, A, &B, &cc);
      spqr_error_handler (&cc);

      Complex *vec = x.fortran_vec ();
      for (volatile octave_idx_type i = 0; i < nc * b_nc; i++)
        vec[i] = reinterpret_cast<Complex *> (X->x)[i];

      cholmod_l_free_sparse (&A, &cc);
      cholmod_l_finish (&cc);

      info = 0;

      return x;

    }

    template <>
    template <>
    OCTAVE_API SparseComplexMatrix
    sparse_qr<SparseMatrix>::min2norm_solve<SparseComplexMatrix,
                                            SparseComplexMatrix>
    (const SparseMatrix& a, const SparseComplexMatrix& b,
     octave_idx_type& info, int order)
    {
      info = -1;

      cholmod_common cc;

      cholmod_l_start (&cc);

      cholmod_sparse *A = ros2ccs (a, &cc);
      cholmod_sparse B = cos2ccs (b);
      cholmod_sparse *X;

      X = SuiteSparseQR_min2norm<Complex> (order, SPQR_DEFAULT_TOL, A, &B, &cc);
      spqr_error_handler (&cc);

      cholmod_l_free_sparse (&A, &cc);
      if (sizeof (octave_idx_type) != sizeof (SuiteSparse_long))
        {
          delete [] reinterpret_cast<SuiteSparse_long *> (B.p);
          delete [] reinterpret_cast<SuiteSparse_long *> (B.i);
        }
      cholmod_l_finish (&cc);

      SparseComplexMatrix ret = ccs2cos(X);

      info = 0;

      return ret;

    }

    template <>
    template <>
    OCTAVE_API ComplexMatrix
    sparse_qr<SparseComplexMatrix>::min2norm_solve<MArray<Complex>,
                                                   ComplexMatrix>
    (const SparseComplexMatrix& a, const MArray<Complex>& b,
     octave_idx_type& info,int order)
    {
      info = -1;
      octave_idx_type b_nc = b.cols ();
      octave_idx_type nc = a.cols ();
      ComplexMatrix x (nc, b_nc);

      cholmod_common cc;

      cholmod_l_start (&cc);

      cholmod_sparse A = cos2ccs (a);
      cholmod_dense B = cod2ccd (b);
      cholmod_dense *X;

      X = SuiteSparseQR_min2norm<Complex> (order, SPQR_DEFAULT_TOL, &A, &B, &cc);
      spqr_error_handler (&cc);

      Complex *vec = x.fortran_vec ();
      for (volatile octave_idx_type i = 0; i < nc * b_nc; i++)
        vec[i] = reinterpret_cast<Complex *> (X->x)[i];

      if (sizeof (octave_idx_type) != sizeof (SuiteSparse_long))
        {
          delete [] reinterpret_cast<SuiteSparse_long *> (A.p);
          delete [] reinterpret_cast<SuiteSparse_long *> (A.i);
        }
      cholmod_l_finish (&cc);

      info = 0;

      return x;

    }

    template <>
    template <>
    OCTAVE_API ComplexMatrix
    sparse_qr<SparseComplexMatrix>::min2norm_solve<MArray<double>,
                                                   ComplexMatrix>
    (const SparseComplexMatrix& a, const MArray<double>& b,
     octave_idx_type& info, int order)
    {
      info = -1;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type nc = a.cols ();
      ComplexMatrix x (nc, b_nc);

      cholmod_common cc;

      cholmod_l_start (&cc);

      cholmod_sparse A = cos2ccs (a);
      cholmod_dense *B = rod2ccd (b, &cc);
      cholmod_dense *X;

      X = SuiteSparseQR_min2norm<Complex> (order, SPQR_DEFAULT_TOL, &A, B, &cc);
      spqr_error_handler (&cc);

      Complex *vec = x.fortran_vec ();

      for (volatile octave_idx_type i = 0; i < nc * b_nc; i++)
       vec[i] = reinterpret_cast<Complex *> (X->x)[i];

      if (sizeof (octave_idx_type) != sizeof (SuiteSparse_long))
        {
          delete [] reinterpret_cast<SuiteSparse_long *> (A.p);
          delete [] reinterpret_cast<SuiteSparse_long *> (A.i);
        }
      cholmod_l_free_dense (&B, &cc);
      cholmod_l_finish (&cc);

      info = 0;

      return x;

    }

    template <>
    template <>
    OCTAVE_API SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::min2norm_solve<SparseComplexMatrix,
                                                   SparseComplexMatrix>
    (const SparseComplexMatrix& a, const SparseComplexMatrix& b,
     octave_idx_type& info, int order)
    {
      info = -1;

      cholmod_common cc;

      cholmod_l_start (&cc);

      cholmod_sparse A = cos2ccs (a);
      cholmod_sparse B = cos2ccs (b);
      cholmod_sparse *X;

      X = SuiteSparseQR_min2norm<Complex> (order, SPQR_DEFAULT_TOL, &A, &B, &cc);
      spqr_error_handler (&cc);

      if (sizeof (octave_idx_type) != sizeof (SuiteSparse_long))
        {
          delete [] reinterpret_cast<SuiteSparse_long *> (A.p);
          delete [] reinterpret_cast<SuiteSparse_long *> (A.i);
          delete [] reinterpret_cast<SuiteSparse_long *> (B.p);
          delete [] reinterpret_cast<SuiteSparse_long *> (B.i);
        }
      cholmod_l_finish (&cc);

      info = 0;

      return ccs2cos (X);

    }

    template <>
    template <>
    OCTAVE_API SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::min2norm_solve<SparseMatrix,
                                                   SparseComplexMatrix>
    (const SparseComplexMatrix& a, const SparseMatrix& b,
     octave_idx_type& info,int order)
    {
      info = -1;

      cholmod_common cc;

      cholmod_l_start (&cc);

      cholmod_sparse A = cos2ccs (a);
      cholmod_sparse *B = ros2ccs (b, &cc);
      cholmod_sparse *X;

      X = SuiteSparseQR_min2norm<Complex> (order, SPQR_DEFAULT_TOL, &A, B, &cc);
      spqr_error_handler (&cc);

      SparseComplexMatrix ret = ccs2cos(X);

      if (sizeof (octave_idx_type) != sizeof (SuiteSparse_long))
        {
          delete [] reinterpret_cast<SuiteSparse_long *> (A.p);
          delete [] reinterpret_cast<SuiteSparse_long *> (A.i);
        }
      cholmod_l_free_sparse (&B, &cc);
      cholmod_l_finish (&cc);

      info = 0;

      return ret;

    }
#endif

    // FIXME: Why is the "order" of the QR calculation as used in the
    // CXSparse function sqr 3 for real matrices and 2 for complex?  These
    // values seem to be required but there was no explanation in David
    // Bateman's original code.

    template <typename SPARSE_T>
    class
    cxsparse_defaults
    {
    public:
      enum { order = -1 };
    };

    template <>
    class
    cxsparse_defaults<SparseMatrix>
    {
    public:
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))
      enum { order = SPQR_ORDERING_DEFAULT };
#elif defined (HAVE_CXSPARSE)
      enum { order = 3 };
#endif
    };

    template <>
    class
    cxsparse_defaults<SparseComplexMatrix>
    {
    public:
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))
      enum { order = SPQR_ORDERING_DEFAULT };
#elif defined (HAVE_CXSPARSE)
      enum { order = 2 };
#endif
    };

    template <typename SPARSE_T>
    template <typename RHS_T, typename RET_T>
    RET_T
    sparse_qr<SPARSE_T>::solve (const SPARSE_T& a, const RHS_T& b,
                                octave_idx_type& info)
    {
#if (defined (HAVE_SPQR) && defined (HAVE_CHOLMOD))

      info = -1;

      octave_idx_type nr = a.rows ();
      octave_idx_type nc = a.cols ();

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      int order = cxsparse_defaults<SPARSE_T>::order;

      if (nr <= 0 || nc <= 0 || b_nc <= 0 || b_nr <= 0)
        (*current_liboctave_error_handler)
          ("matrix dimension with negative or zero size");

      if ( nr != b_nr)
        (*current_liboctave_error_handler)
          ("matrix dimension mismatch in solution of minimum norm problem");

      info = 0;

      return min2norm_solve<RHS_T, RET_T> (a, b, info, order);

#elif defined (HAVE_CXSPARSE)

      info = -1;

      octave_idx_type nr = a.rows ();
      octave_idx_type nc = a.cols ();

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      int order = cxsparse_defaults<SPARSE_T>::order;

      if (nr < 0 || nc < 0 || nr != b_nr)
        (*current_liboctave_error_handler)
          ("matrix dimension mismatch in solution of minimum norm problem");

      if (nr == 0 || nc == 0 || b_nc == 0)
        {
          info = 0;

          return RET_T (nc, b_nc, 0.0);
        }
      else if (nr >= nc)
        {
          sparse_qr<SPARSE_T> q (a, order);

          return q.ok () ? q.tall_solve<RHS_T, RET_T> (b, info) : RET_T ();
        }
      else
        {
          sparse_qr<SPARSE_T> q (a.hermitian (), order);

          return q.ok () ? q.wide_solve<RHS_T, RET_T> (b, info) : RET_T ();
        }

#else

      octave_unused_parameter (a);
      octave_unused_parameter (b);
      octave_unused_parameter (info);

      return RET_T ();

#endif
    }

    //explicit instantiations of static member function solve
    template
    OCTAVE_API Matrix
    sparse_qr<SparseMatrix>::solve<MArray<double>, Matrix>
    (const SparseMatrix& a, const MArray<double>& b, octave_idx_type& info);

    template
    OCTAVE_API SparseMatrix
    sparse_qr<SparseMatrix>::solve<SparseMatrix, SparseMatrix>
    (const SparseMatrix& a, const SparseMatrix& b, octave_idx_type& info);

    template
    OCTAVE_API ComplexMatrix
    sparse_qr<SparseMatrix>::solve<MArray<Complex>, ComplexMatrix>
    (const SparseMatrix& a, const MArray<Complex>& b, octave_idx_type& info);

    template
    OCTAVE_API SparseComplexMatrix
    sparse_qr<SparseMatrix>::solve<SparseComplexMatrix, SparseComplexMatrix>
    (const SparseMatrix& a, const SparseComplexMatrix& b,
     octave_idx_type& info);

    template
    OCTAVE_API ComplexMatrix
    sparse_qr<SparseComplexMatrix>::solve<MArray<Complex>, ComplexMatrix>
    (const SparseComplexMatrix& a, const MArray<Complex>& b,
     octave_idx_type& info);

    template
    OCTAVE_API SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::solve<
    SparseComplexMatrix, SparseComplexMatrix>
    (const SparseComplexMatrix& a, const SparseComplexMatrix& b,
     octave_idx_type& info);

    template
    OCTAVE_API ComplexMatrix
    sparse_qr<SparseComplexMatrix>::solve<MArray<double>, ComplexMatrix>
    (const SparseComplexMatrix& a, const MArray<double>& b,
     octave_idx_type& info);

    template
    OCTAVE_API SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::solve<SparseMatrix, SparseComplexMatrix>
    (const SparseComplexMatrix& a, const SparseMatrix& b,
     octave_idx_type& info);

    //explicit instantiations of member function E_MAT
    template
    OCTAVE_API SparseMatrix
    sparse_qr<SparseMatrix>::E_MAT (void) const;

    template
    OCTAVE_API SparseMatrix
    sparse_qr<SparseComplexMatrix>::E_MAT (void) const;

    template <typename SPARSE_T>
    template <typename RHS_T, typename RET_T>
    RET_T
    sparse_qr<SPARSE_T>::tall_solve (const RHS_T& b, octave_idx_type& info) const
    {
      return m_rep->template tall_solve<RHS_T, RET_T> (b, info);
    }

    template <typename SPARSE_T>
    template <typename RHS_T, typename RET_T>
    RET_T
    sparse_qr<SPARSE_T>::wide_solve (const RHS_T& b, octave_idx_type& info) const
    {
      return m_rep->template wide_solve<RHS_T, RET_T> (b, info);
    }

    // Explicitly instantiate all member functions

    template OCTAVE_API sparse_qr<SparseMatrix>::sparse_qr (void);
    template OCTAVE_API
    sparse_qr<SparseMatrix>::sparse_qr (const SparseMatrix& a, int order);
    template OCTAVE_API bool sparse_qr<SparseMatrix>::ok (void) const;
    template OCTAVE_API ColumnVector sparse_qr<SparseMatrix>::E (void) const;
    template OCTAVE_API SparseMatrix sparse_qr<SparseMatrix>::V (void) const;
    template OCTAVE_API ColumnVector sparse_qr<SparseMatrix>::Pinv (void) const;
    template OCTAVE_API ColumnVector sparse_qr<SparseMatrix>::P (void) const;
    template OCTAVE_API SparseMatrix
    sparse_qr<SparseMatrix>::R (bool econ) const;
    template OCTAVE_API Matrix
    sparse_qr<SparseMatrix>::C (const Matrix& b, bool econ) const;
    template OCTAVE_API Matrix sparse_qr<SparseMatrix>::Q (bool econ) const;

    template OCTAVE_API sparse_qr<SparseComplexMatrix>::sparse_qr (void);
    template OCTAVE_API
    sparse_qr<SparseComplexMatrix>::sparse_qr
    (const SparseComplexMatrix& a, int order);
    template OCTAVE_API bool sparse_qr<SparseComplexMatrix>::ok (void) const;
    template OCTAVE_API ColumnVector
    sparse_qr<SparseComplexMatrix>::E (void) const;
    template OCTAVE_API SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::V (void) const;
    template OCTAVE_API ColumnVector
    sparse_qr<SparseComplexMatrix>::Pinv (void) const;
    template OCTAVE_API ColumnVector
    sparse_qr<SparseComplexMatrix>::P (void) const;
    template OCTAVE_API SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::R (bool econ) const;
    template OCTAVE_API ComplexMatrix
    sparse_qr<SparseComplexMatrix>::C (const ComplexMatrix& b, bool econ) const;
    template OCTAVE_API ComplexMatrix
    sparse_qr<SparseComplexMatrix>::Q (bool econ) const;

    Matrix
    qrsolve (const SparseMatrix& a, const MArray<double>& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseMatrix>::solve<MArray<double>, Matrix> (a, b,
                                                                     info);
    }

    SparseMatrix
    qrsolve (const SparseMatrix& a, const SparseMatrix& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseMatrix>::solve<SparseMatrix, SparseMatrix> (a, b,
                                                                         info);
    }

    ComplexMatrix
    qrsolve (const SparseMatrix& a, const MArray<Complex>& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseMatrix>::solve<MArray<Complex>,
                                            ComplexMatrix> (a, b, info);
    }

    SparseComplexMatrix
    qrsolve (const SparseMatrix& a, const SparseComplexMatrix& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseMatrix>::solve<SparseComplexMatrix,
                                            SparseComplexMatrix> (a, b, info);
    }

    ComplexMatrix
    qrsolve (const SparseComplexMatrix& a, const MArray<double>& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseComplexMatrix>::solve<MArray<double>,
                                                   ComplexMatrix> (a, b, info);
    }

    SparseComplexMatrix
    qrsolve (const SparseComplexMatrix& a, const SparseMatrix& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseComplexMatrix>::solve<SparseMatrix,
                                                   SparseComplexMatrix>
                                             (a, b, info);
    }

    ComplexMatrix
    qrsolve (const SparseComplexMatrix& a, const MArray<Complex>& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseComplexMatrix>::solve<MArray<Complex>,
                                                   ComplexMatrix> (a, b, info);
    }

    SparseComplexMatrix
    qrsolve (const SparseComplexMatrix& a, const SparseComplexMatrix& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseComplexMatrix>::solve<SparseComplexMatrix,
                                                   SparseComplexMatrix>
                                             (a, b, info);
    }
  }
}
